Geometry Review DPMA 3

TRIGONOMETRIC RATIOS

100

A right triangle has angle C=30∘. The opposite side to angle C is 7, and the hypotenuse is 14. What is sin⁡C?

sin⁡C=7/14=1/2

200

In a right triangle, angle C is acute. The adjacent side to angle C is 9, and the hypotenuse is 15. Find cos⁡C.

cos⁡C=9/15=3/5

300

A right triangle has angle C=40∘. The opposite side to angle C is 12, and the adjacent side is 16. What is tan⁡C?

tan⁡C=12/16=3/4

400

In a right triangle, the opposite side to angle C is 5, and sin⁡C=5/13. Find the hypotenuse.

Hypotenuse = 13

500

A right triangle has hypotenuse 20. Angle C is such that cos⁡C=35. Find the lengths of the opposite and adjacent sides.

Adjacent = 20⋅35=12  

Opposite = 20⋅45=16

QUADRILATERALS

100

A rectangle has a length of 12 and a width of 5. What is its area?

12×5=60

200

A square has a side length of 9. What is its perimeter?

4×9=36

300

A parallelogram has a base of 14 and a height of 6. What is its area?

14×6=84

400

A trapezoid has bases of 10 and 18, and a height of 7. Find the area.

12(10+18)(7)=12(28)(7)=98

500

A quadrilateral has opposite sides both equal and parallel, and its diagonals bisect each other. What type of quadrilateral must it be?

Parallelogram

ARC LENGTH

100

A circle has a radius of 10 and a central angle of 36∘. Find the arc length.

36/360⋅2π(10)=2π=6.28

200

A circle has a radius of 7 and a central angle of 90∘. What is the arc length?

90/360⋅2π(7)=14⋅14π=3.5π=10.99

300

A circle has a diameter of 20. A central angle intercepts an arc of length 8π. What is the measure of the central angle?

Radius = 10 Arc length formula: s=θ/360⋅2πr  8π=θ/360⋅20π  θ=144∘

400

A circle has radius 12. The arc length is 6π. Find the central angle measure.

6π=θ/360⋅24π  θ=90∘

500

A circle has circumference 40π. A central angle intercepts an arc of length 5π. Find the measure of the central angle.

5π/40π=θ/360  θ=45∘

AREA OF A SECTOR

100

A circle has radius 8 and a central angle of 45∘. Find the area of the sector.

45/360⋅π(82)=1/8⋅64π=8π=25.13

200

A circle has radius 5 and a central angle of 90∘. What is the area of the sector

90/360⋅π(25)=14⋅25π=6.25π=19.6

300

A circle has radius 12. The area of a sector is 36π. Find the measure of the central angle.

Sector area formula: θ/360⋅π(122)  36π=θ/360⋅144π  θ=90∘

400

A circle has radius 10. A sector has a central angle of 72∘. Find the area of the sector.

72/360⋅π(100)=15⋅100π=20π=62.83

500

A sector has area 15π and central angle 54∘. Find the radius of the circle.

15π=54/360⋅πr2

15=320r2

r2=100⇒r=10

TRIANGLE MIDSEGMENT THEOREM

100

In triangle ABC, D is the midpoint of AB and E is the midpoint of AC. What is the relationship between segment DE and side BC?

DE is parallel to BC.

200

In triangle ABC, DE is a midsegment. If BC=18, what is the length of DE?

DE=12(18)=9

300

In triangle ABC, DE is a midsegment. If DE=7, what is the length of the side it is parallel to?

Parallel side = 2×7=14

400

In triangle ABC, D is the midpoint of AB. If DE∥BC and DE=6, but the student claims BC=10, what mistake did the student make?

They forgot the midsegment is half the length of the parallel side. Correct BC=12.

500

In triangle ABC, DE is a midsegment. If BC=24 and the perimeter of triangle ADE is 30, find the perimeter of triangle ABC.

Midsegment triangle is similar to the big triangle with scale factor 12. So the big triangle’s perimeter is double: 30×2=60